Middle-obstacle approach of mapping phase-field model unto its sharp interface counterpart

TL;DR

This paper introduces a middle-obstacle approach to improve phase-field models for alloy solidification, enabling accurate interface sharpening and better simulation of both equilibrium and non-equilibrium solidification processes.

Contribution

The study develops a novel middle-obstacle method that enhances phase-field models by sharpening diffuse interfaces and accurately capturing solute partitioning during solidification.

Findings

Superior convergence of dendrite tip under slow solidification.

Accurate partition coefficients under rapid solidification.

Effective interface sharpening across cooling conditions.

Abstract

A new diffuse interface model has been proposed in this study for simulating binary alloy solidification under universal cooling conditions, involving both equilibrium and non-equilibrium solute partitioning. Starting from the Gibbs-Thomson equation, which is the classical theory that describes the dynamics of a sharp interface, the phase-field equation is derived using a traveling wave solution that represents a diffuse interface. To tackle the spurious effects caused by the variation of liquid concentration within the diffuse interface with artificial width, a middle obstacle is introduced to sharpen the diffuse interface and an invariant liquid concentration can be found for determining a constant undercooling in the interface normal direction. For slow solidification under equilibrium conditions, the convergence performance of the dendrite tip shows superior invulnerability to the width effect of the diffuse interface. For rapid solidification under non-equilibrium conditions, the output partition coefficients obtained from the steady-state concentration profiles agree with the input velocity-dependent function. The proposed model is promising to be an indispensable tool for the development of advanced alloy materials through the microstructure control of solidification under a wide range of cooling conditions.